Note that \(m<n\) .
By [1]}'s inequality, we have
\(P\left(|d_i-\mathbb {E}(d_i)|\ge \sqrt{n\log {n}}\right)\le 2\exp {\lbrace -\frac{2n\log {n}}{m}\rbrace }\le \frac{2}{n^{2n/m}} \le \frac{2}{n^2}.\) 
